Choice Number and Energy of Graphs

Details Choice Number and Energy of Graphs Choice Number and Energy of Graphs

2007-12-06

arxiv.org/abs/0712.0920v1

Mathematics

Combinatorics

to appear in Linear Algebra and its Applications

Scientific paper

The energy of a graph G, denoted by E(G), is defined as the sum of the absolute values of all eigenvalues of G. It is proved that E(G)>= 2(n-\chi(\bar{G}))>= 2(ch(G)-1) for every graph G of order n, and that E(G)>= 2ch(G) for all graphs G except for those in a few specified families, where \bar{G}, \chi(G), and ch(G) are the complement, the chromatic number, and the choice number of G, respectively.

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